Amid the gasping and the stroking of chins that have greeted Fiona Banner's new installation of a dangling Harrier jet in Tate Britain's Duveen Hall, there has been another, more basic reaction. Namely: how the hell did they do that?

And the answer, of course, is with great care. "We worked with a specialist rigging company," explains curator Lizzie Carey-Thomas, "to devise a way to break the plane down into parts that were small enough to get into the building, and then find a way to seamlessly put them back together."

First of all, the company, whose normal business is assembling special effects and lighting systems in large arenas, stripped the Harrier of all its innards. After this, the jet was dismembered and strengthened internally to prevent it collapsing on itself when hung. Once inside the Tate, the wing section and the rear part of the fuselage were reconnected, before being hoisted up on pulleys. The tail fins and nose cone were added last. "So it was sort of done in the air, really," says Carey- Thomas, "and invisibly."

While it wasn't the heaviest thing Carey-Thomas's team has worked on – she cites massive sculptures by Anthony Caro and Phillip King as being particularly challenging to move – the Harrier was "one of the most complex".

Needless to say, the entire project has also been verified by structural engineers, who reinforced the area around the skylight with "secondary steelwork". And yet the Harrier does hang from just two wires. Is Carey-Thomas sure it's safe? "It's gone through a rigorous process of checks," she insists.

It could still swing about a bit, however? "If you gave it a very good knock you could probably get some movement out of it," she says. But people aren't allowed to? "They're not allowed to do that. No." Can they lie underneath it and frighten themselves, in the manner of our critic Adrian Searle? "As long as they don't touch it," she says, with complete confidence, "they can do whatever they like."

Harrier and Jaguar, Tate Britain's 2010 Duveens commission, is an ambitious new work by the artist Fiona Banner that challenges the aesthetic and physical expectations of the neoclassical Duveen galleries